His parents were Benjamin and Celia (Solomont) Kaplan. They had three sons Joseph, Archie, and Kivie, who was the youngest. In 1924 the sons took over their father’s leather business. Kivie Kaplan retired from the family business in 1962.
In 1925 he married Emily Rogers. They had three children.
Kaplan joined the NAACP in 1932 and became a member of their National Board in 1954. NAACP membership historically has been open to all races with Jews playing a major role in the organization's leadership. In 1966 he became president of the NAACP holding that office until his death in 1975.